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On the existence of doubling measures with certain regularity properties
Author(s):
Per
Bylund;
Jaume
Gudayol
Journal:
Proc. Amer. Math. Soc.
128
(2000),
3317-3327.
MSC (2000):
Primary 28C15;
Secondary 54E45, 54F45
Posted:
May 11, 2000
MathSciNet review:
1676303
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Abstract:
Given a compact pseudo-metric space, we associate to it upper and lower dimensions, depending only on the pseudo-metric. Then we construct a doubling measure for which the measure of a dilated ball is closely related to these dimensions.
References:
-
- [Byl]
- Per Bylund, Besov spaces and measures on arbitrary closed sets, Doctoral Thesis No 8, 1994, Department of Mathematics, University of Umeå, Sweden. MR 95k:46046
- [Dyn]
- E. M. Dynkin, Free interpolation by functions with derivatives in
 , J. Soviet Math. 27 (1984), 2475-2481. - [Gud]
- Jaume Gudayol, Boundary behaviour of functions in Hardy-Sobolev spaces, doctoral dissertation, Universitat de Barcelona, 1997.
- [Jon]
- Alf Jonsson, Besov spaces on closed subsets of
 , Transactions of the AMS 41 (1994), no. 1, 355-370. MR 94c:46065 - [J-W]
- Alf Jonsson and Hans Wallin, Function spaces on subsets of
 , Math. Reports Volume 2, Part 1, Harwood Academics Publ. GmbH, 1984. - [Lar]
- D.G. Larman, A new theory of dimension, Proc. London Math. Soc. (3rd series) 17 (1967), 178-192. MR 34:3540
- [L-S]
- J. Luukkainen and E. Saksman, Every complete doubling metric space carries a doubling measure, Proceedings of the AMS 126 (1998), 531-534. MR 99c:28009
- [V-K]
- A.L. Vol'berg and S.V. Konyagin, On measures with the doubling condition, Math. USSR Izvestiya 30 (1988), 629-638. MR 88i:28006
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Additional Information:
Per
Bylund
Affiliation:
Department of Mathematics, University of Umeå, S-90187 Umeå, Sweden
Email:
Per.Bylund@math.umu.se
Jaume
Gudayol
Affiliation:
Departament de Matèmatica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain
Email:
gudayol@mat.ub.es
DOI:
10.1090/S0002-9939-00-05405-8
PII:
S 0002-9939(00)05405-8
Received by editor(s):
May 14, 1998
Received by editor(s) in revised form:
January 4, 1999
Posted:
May 11, 2000
Additional Notes:
The second author is partially supported by MEC grant PB95-0956-C02-01 and CIRIT grant GRQ94-2014.
Communicated by:
Dale Alspach
Copyright of article:
Copyright
2000,
American Mathematical Society
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